The main goal of the present paper is to show for general deformations that the stability condition (REF ) found in [1]} by the energy method is not only sufficient but also necessary for uniform stability. It is clear that this can be done only by spectral analysis. However, it seems that the classical tools towards the test of the Lopatinski condition and the uniform Lopatinski condition, as it is described in [2]}, [3]}, [4]}, [5]}, are hardly applicable to the model of elastodynamics because of its big technical complexity. We overcome this difficulty by using equivalent definitions of the Lopatinski condition and the uniform Lopatinski condition proposed in [6]} for symmetric hyperbolic systems having the 1-shock property. Roughly speaking, the main idea of [6]} borrowed from [8]} is to carry all the calculations over the unique characteristic incoming in the shock in the region behind of the shock wave.
